Partial Derivative Calculator

Partial derivatives are how calculus handles functions that depend on more than one variable, and this calculator finds them for a function of x and y at any point you choose. Enter the function and the coordinates of a point, and it returns the partial derivative with respect to x, the partial derivative with respect to y, and the gradient, the vector that bundles them together, all updating as you type. The idea is beautifully simple once it clicks: to find the partial derivative with respect to one variable, you treat every other variable as a fixed constant and differentiate as normal. So the partial with respect to x measures how the function changes if you nudge x while holding y still, the slope of the surface in the x-direction, and the partial with respect to y does the same in the y-direction. Together these slopes describe how a surface tilts in space, which is why partial derivatives are central to multivariable calculus, optimisation, physics and economics, anywhere a quantity depends on several inputs at once. The gradient, made from the two partials, has a lovely meaning of its own: it points in the direction in which the function increases fastest, and its length is how steep that steepest climb is, the principle behind gradient-based methods used throughout machine learning and engineering. The calculator works numerically, nudging each variable a tiny amount to measure the response, so it handles any function you type, with the caret for powers and the usual sin, cos, sqrt, exp and ln. That makes it genuinely useful for university students learning multivariable calculus and checking work, and for anyone needing a quick, accurate partial derivative at a point. The method and a worked example are explained clearly below.

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Use x, y, ^ for powers, * for multiply, and functions like sin, cos, sqrt, exp, ln. Partials are computed numerically.